<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262022000100093</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v56n1.105621</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[On the invariant rational curves of a certain family of polynomial differential equations]]></article-title>
<article-title xml:lang="es"><![CDATA[Sobre las curvas racionales invariantes de cierta familia de ecuaciones diferenciales]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Díaz-Marín]]></surname>
<given-names><![CDATA[Homero]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Osuna]]></surname>
<given-names><![CDATA[Osvaldo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Michoacana de San Nicolás de Hidalgo  ]]></institution>
<addr-line><![CDATA[Morelia ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<volume>56</volume>
<numero>1</numero>
<fpage>93</fpage>
<lpage>111</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262022000100093&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262022000100093&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262022000100093&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this work, we present sufficient conditions to determine if the limit cycles of certain differential systems in the plane are algebraic or not. In particular, we obtain criteria such that the limit cycles of equations derived from predatory prey models with rational functional response are necessarily transcendental ovals.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este trabajo presentamos condiciones necesarias y suficientes para determinar si los ciclos límite de ciertas ecuaciones diferenciales en el plano son algebraicos o no. Particularmente, obtenemos criterios para que ciclos límite de ciertas ecuaciones derivadas de modelos depredador - presa con ciertos funcionales racionales de respuesta sean necesariamente óvalos trascendentes.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[algebraic limit-cycles]]></kwd>
<kwd lng="en"><![CDATA[Puiseux series]]></kwd>
<kwd lng="en"><![CDATA[Newton polygon]]></kwd>
<kwd lng="en"><![CDATA[predator-prey models]]></kwd>
<kwd lng="en"><![CDATA[functional-response]]></kwd>
<kwd lng="es"><![CDATA[ciclos límte algebraicos]]></kwd>
<kwd lng="es"><![CDATA[series de Puiseux]]></kwd>
<kwd lng="es"><![CDATA[polígono de Newton]]></kwd>
<kwd lng="es"><![CDATA[modelos depredador-presa]]></kwd>
<kwd lng="es"><![CDATA[funcional de respuesta]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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